Symmetries and Differential Invariants for Viscid Flows on a Curve

TL;DR

This paper investigates the symmetries and differential invariants of viscous fluid flows on curves, analyzing how these properties depend on thermodynamic states and classifying these states.

Contribution

It introduces a classification of thermodynamic states for viscous flows on curves and derives symmetry algebras and differential invariants related to these flows.

Findings

Symmetry algebras for viscous flows on curves are characterized.

Differential invariants depend on thermodynamic states.

A classification scheme for thermodynamic states is provided.

Abstract

In this paper, flows of a viscid fluids on curves are considered. Symmetry algebras and the corresponding fields of differential invariants are found. We study their dependence on thermodynamic states of media, and provide classification of thermodynamic states.